# Teaching and learning in uncertainty

## TL;DR

This paper models social learning with a teacher and student under uncertainty, analyzing different teaching strategies and their effectiveness using large deviation theory, revealing conditions where simpler methods outperform more complex ones.

## Contribution

It introduces a model for teaching under uncertainty with noisy channels and compares simple and complex teaching strategies, providing exact learning rates and insights into optimal strategies.

## Key findings

- Low-effort strategy can outperform high-effort strategy in certain regimes.
- Exact learning rates are derived using large deviation theory.
- A conjecture on the optimal learning rate for joint strategies is proposed.

## Abstract

We investigate a simple model for social learning with two agents: a teacher and a student. The teacher's goal is to teach the student the state of the world; however, the teacher himself is not certain about the state of the world and needs to simultaneously learn this parameter and teach it to the student. We model the teacher's and student's uncertainties via noisy transmission channels, and employ two simple decoding strategies for the student. We focus on two teaching strategies: a "low-effort" strategy of simply forwarding information, and a "high-effort" strategy of communicating the teacher's current best estimate of the world at each time instant, based on his own cumulative learning. Using tools from large deviation theory, we calculate the exact learning rates for these strategies and demonstrate regimes where the low-effort strategy outperforms the high-effort strategy. Finally, we present a conjecture concerning the optimal learning rate for the student over all joint strategies between the student and the teacher.